I'm looking for a travel guide (i.e. book) to Kaliningrad. Are there any particularly useful English-language references for visitors to Kaliningrad? I am particularly interested in any remnants of the old Königsberg.

Königsberg was destroyed during WWII, and then reconstructed. So there are some old houses, but not as many as you can hope to find.

As Mark said, you should start with Cathedral, and Kant's Tomb.
After that you can continue with some forts inside and outside the city, and visit some small city in Kaliningrad region. Especially I recommend the Svetlogorsk.

Although I still consult the default guides (e.g. lonely planet, rough guide), I find my self more and more to rely on online resources, specifically build around satnav devices.

My three favorites are 1. Geocaching.com, 2. routeyou.com, and 3. Everytrail.com.
Geocaching is nice, specifically if locals engage in this fun activity. Then again, you need to speak russian to appreciate the caches to the fullest.

So although these three online resources don't provide an extensive source on written descriptions, all provide interesting focal points in any destination, at least in my experience.